Title:
Spatial structure increases the waiting time for cancer

Abstract: Cancer results from a sequence of genetic and epigenetic changes which lead
to a variety of abnormal phenotypes including increased proliferation and
survival of somatic cells, and thus, to a selective advantage of pre-cancerous
cells. The notion of cancer progression as an evolutionary process has been
experiencing increasing interest in recent years. Many efforts have been made
to better understand and predict the progression to cancer using mathematical
models; these mostly consider the evolution of a well-mixed cell population,
even though pre-cancerous cells often evolve in highly structured epithelial
tissues. We propose a novel model of cancer progression that considers a
spatially structured cell population where clones expand via adaptive waves.
This model is used to asses two different paradigms of asexual evolution that
have been suggested to delineate the process of cancer progression. The
standard scenario of periodic selection assumes that driver mutations are
accumulated strictly sequentially over time. However, when the mutation supply
is sufficiently high, clones may arise simultaneously on distinct genetic
backgrounds, and clonal adaptation waves interfere with each other. We find
that in the presence of clonal interference, spatial structure increases the
waiting time for cancer, leads to a patchwork structure of non-uniformly sized
clones, decreases the survival probability of virtually neutral (passenger)
mutations, and that genetic distance begins to increase over a characteristic
length scale, determined here. These characteristic features of clonal
interference may help to predict the onset of cancers with pronounced spatial
structure and to interpret spatially-sampled genetic data obtained from
biopsies. Our estimates suggest that clonal interference likely occurs in the
progressing colon cancer, and possibly other cancers where spatial structure
matters.